An optimum design of deep-space downlinks affected by tropospheric attenuation

In the paper, we propose an optimum design of deep–space downlinks made with 2 hops, at Ka band and above, in which each hop should be designed for providing half of the total noise–to–signal power ratio. We have derived this result from maximizing the ratio between the tropospheric attenuation in the 2–hop downlink and that in the 1–hop downlink. The design of the 1st hop (free–space) of the 2–hop downlink can reduce the spacecraft power, for the same antennas physical size, by increasing the carrier frequency from Ka band (32 GHz) to W band (80 GHz). This choice is not available in 1–hop downlink design because of the huge Earth tropospheric attenuation expected in the W frequency band. To show a practical design, we have applied the theory to compare 1–hop downlink design at 32 GHz to 2–hop downlink design that adopts 32 or 80 GHz in the 1st hop. The calculations refer to spacecrafts located at 2 astronomical units ( km, about planet Mars) and to NASA and ESA receiving stations located in Goldstone (California), Cebreros (Madrid, Spain), Canberra and New Norcia (Australia). At 0.1% outage probability, in an average year or in the worst month, 1–hop downlinks show performance critical or close to fail, because of the large tropospheric attenuation (except at Goldstone), while 2–hop downlinks always work.